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<p>The Euler’s equation is</p>
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\begin{equation}
L[y]=x^2 y^{\prime \prime}+\alpha x y^{\prime}+\beta y=0, \quad \alpha, \beta~\textrm{are constants.}\tag{5.4.1}
\end{equation}
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<p class="continuation">In the following, we assume that <span class="process-math">\(x&gt;0\text{.}\)</span> If <span class="process-math">\(x&lt;0\text{,}\)</span> by a change of variables <span class="process-math">\(t=-x (&gt;0)\text{,}\)</span> we obtain the same equation.</p>
<span class="incontext"><a href="sec5_4.html#p-225" class="internal">in-context</a></span>
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